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2-1: Fixed, Variable, and Average Costs

Midstate University is trying to decide whether to allow 100 more students into the

university. Tuition is $5000 per year. The controller has determined the following schedule of

costs to educate students:

Number of Students Total Costs

4000 $30,000,000

4100 30,300,000

4200 30,600,000

4300 30,900,000

The current enrollment is 4200 students. The president of the university has calculated the cost

per student in the following manner: $30,600,000/4200 students = $7286 per student. The

president was wondering why the university should accept more students if the tuition is only

$5000.

Required:

a. What is wrong with the president’s calculation?

b. What are the fixed and variable costs of operating the university?

2-2: Opportunity Costs

The First Church has been asked to operate a homeless shelter in part of the church. To

operate a homeless shelter the church would have to hire a full time employee for $1,200/month

to manage the shelter. In addition, the church would have to purchase $400 of supplies/month

for the people using the shelter. The space that would be used by the shelter is rented for

wedding parties. The church averages about 5 wedding parties a month that pay rent of $200 per

party. Utilities are normally $1,000 per month. With the homeless shelter, the utilities will

increase to $1,300 per month.

What is the opportunity cost to the church of operating a homeless shelter in the church?

2-3: Fixed and Variable Costs

The university athletic department has been asked to host a professional basketball game

at the campus sports center. The athletic director must estimate the opportunity cost of holding

the event at the sports center. The only other event scheduled for the sports center that evening

is a fencing match that would not have generated any additional costs or revenues. The fencing

match can be held at the local high school, but the rental cost of the high school gym would be

$200. The athletic director estimates that the professional basketball game will require 20 hours

of labor to prepare the building. Clean-up depends on the number of spectators. The athletic

director estimates the time of clean-up to be equal to 2 minutes per spectator. The labor would

be hired especially for the basketball game and would cost $8 per hour. Utilities will be $500

greater if the basketball game is held at the sports center. All other costs would be covered by

the professional basketball team.

Required:

a. What is the variable cost of having one more spectator?

b. What is the opportunity cost of allowing the professional basketball team to use the sports

center if 10,000 spectators are expected?

c. What is the opportunity cost of allowing the professional basketball team to use the sports

center if 12,000 spectators are expected?

2-4: Opportunity Cost of Attracting Industry

The Itagi Computer Company From Japan is looking to build a factory for making CDROM’s in the United States. The company is concerned about the safety and well-being of its

employees and wants to locate in a community with good schools. The company also wants the

factory to be profitable and is looking for subsidies from potential communities. Encouraging

new business to create jobs for citizens is important for communities, especially communities

with high unemployment.

Wellville has not been very well since the shoe factory left town. The city officials have

been working on a deal with Itagi to get the company to locate in Wellville. Itagi officials have

identified a 20 acre undeveloped site. The city has tentatively agreed to buy the site for $50,000

for Itagi and not require any payment of property taxes on the factory by Itagi for the first five

years of operation. The property tax deal will save Itagi $3,000,000 in taxes over the five years.

This deal was leaked to the local newspaper. The headlines the next day were: “Wellville Gives

Away $3,000,000+ to Japanese Company”.

Required:

a. Do the headlines accurately describe the deal with Itagi?

b. What are the relevant costs and benefits to the citizens of Wellville of making this deal?

2-5: Cost, Volume, Profit Analysis

With the possibility of the US Congress relaxing restrictions on cutting old growth, a

local lumber company is considering an expansion of its facilities. The company believes it can

sell lumber for $0.18/board foot. A board foot is a measure of lumber. The tax rate for the

company is 30 percent. The company has the following two opportunities:

â€¢ Build Factory A with annual fixed costs of $20 million and variable costs of

$0.10/board foot. This factory has an annual capacity of 500 million board feet.

â€¢ Build Factory B with annual fixed costs of $10 million and variable costs of

$0.12/board foot. This factory has an annual capacity of 300 million board feet.

Required:

a. What is the break-even point in board feet for Factory A?

b. If the company wants to generate an after tax profit of $2 million with Factory B, how

many board feet would the company have to process and sell?

c. If demand for lumber is uncertain, which factory is riskier?

d. At what level of board feet would the after-tax profit of the two factories be the same?

2-6: Cost, Volume, Profit Analysis

Leslie Mittelberg is considering the wholesaling of a leather handbag from Kenya. She

must travel to Kenya to check on quality and transportation. The trip will cost $3000. The cost

of the handbag is $10 and shipping to the United States can occur through the postal system for

$2 per handbag or through a freight company which will ship a container that can hold up to a

1000 handbags at a cost of $1000. The freight company will charge $1000 even if less than

1000 handbags are shipped. Leslie will try to sell the handbags to retailers for $20. Assume

there are no other costs and benefits.

Required:

a. What is the break-even point if shipping is through the postal system?

b. How many units must be sold if Leslie uses the freight company and she wants to have a

profit of $1000?

c. At what output level would the two shipping methods yield the same profit?

d. Suppose a large discount store asks to buy an additional 1000 handbags beyond normal

sales. Which shipping method should be used and what is the minimum sales price

Leslie should consider in selling those 1000 handbags?

2-7: Cost, Volume, Profit Analysis

Kalifo Company manufactures a line of electric garden tools that are sold in general

hardware stores. The company’s controller, Sylvia Harlow, has just received the sales forecast

for the coming year for Kalifo’s three products: weeders, hedge clippers, and leaf blowers.

Kalifo has experienced considerable variations in sales volumes and variable costs over the past

two years, and Harlow believes the forecast should be carefully evaluated from a cost-volumeprofit viewpoint. The preliminary budget information for 1996 is presented below.

Weeders Hedge Clippers

Leaf

Blowers

Unit sales 50,000 50,000 100,000

Unit selling price $28.00 $36.00 $48.00

Variable manufacturing cost per unit 13.00 12.00 25.00

Variable selling cost per unit 5.00 4.00 6.00

For 1996, Kalifo’s fixed factory overhead is budgeted at $2 million, and the company’s

fixed selling and administrative expenses are forecast to be $600,000. Kalifo has a tax rate of 40

percent.

Required:

a. Determine Kalifo Co.’s budgeted net income for 1996.

b. Assuming that the sales mix remains as budgeted, determine how many units of each

product Kalifo must sell in order to break even in 1996.

c. Determine the total dollar sales Kalifo must sell in 1996 in order to earn an after-tax net

income of $450,000.

d. After preparing the original estimates, Kalifo determines that its variable manufacturing

cost of leaf blowers will increase 20 percent and the variable selling cost of hedge

clippers can be expected to increase $1 per unit. However, Kalifo has decided not to

change the selling price of either product. In addition, Kalifo learns that its leaf blower is

perceived as the best value on the market, and it can expect to sell three times as many

leaf blowers as any other product. Under these circumstances, determine how many units

of each product Kalifo will have to sell to break even in 1996.

e. Explain the limitations of cost-volume-profit analysis that Sylvia Harlow should consider

when evaluating Kalifo’s 1996 budget.

Source: CMA adapted.

2-8: Breakeven and Cost-Volume-Profit with Taxes

DisKing Company is a retailer for video disks. The projected after-tax net income for the

current year is $120,000 based on a sales volume of 200,000 video disks. DisKing has been

selling the disks at $16 each. The variable costs consist of the $10 unit purchase price of the

disks and a handling cost of $2 per disk. DisKingâ€™s annual fixed costs are $600,000 and DisKing

is subject to a 40 percent income tax rate.

Management is planning for the coming year, when it expects that the unit purchase price

of the video disks will increase 30 percent.

Required:

a. Calculate DisKing Companyâ€™s break-even point for the current year in number of video

disks.

b. Calculate the increased after-tax income for the current year from an increase of 10

percent in projected unit sales volume.

c. If the unit selling price remains at $16, calculate the volume of sales in dollars that

DisKing Company must achieve in the coming year to maintain the same after-tax net

income as projected for the current year.

Source: CMA adapted

2-9: Cost-volume-profit of a Make/buy Decision

Elly Industries is a multiproduct company that currently manufactures 30,000 units of

Part MR24 each month for use in production. The facilities now being used to produce Part

MR24 have affixed monthly cost of $150,000 and a capacity to produce 84,000 units per month.

If Elly were to buy Part MR24 from an outside supplier, the facilities would be idle, but its fixed

costs would continue at 40 percent of its present amount. The variable production costs of Part

MR24 are $11 per unit.

Required:

a. If Elly Industries continues to use 30,000 units of Part MR24 each month, it would

realize a net benefit by purchasing Part MR24 from an outside supplier only if the

supplierâ€™s unit price is less than how much?

b. If Elly Industries can obtain Part MR24 from an outside supplier at a unit purchase price

of $12.875, what is the monthly usage at which it will be indifferent between purchasing

and making Part MR24?

Source: CMA adapted

2-10: Opportunity Cost of Purchase Discounts and Lost Sales

Winter Company is a medium-size manufacturer of disk drives that are sold to computer

manufacturers. At the beginning of 2010, Winter began shipping a much-improved disk drive,

Model W899. The W899 was an immediate success and accounted for $5 million in revenues

for Winter in 2010.

While the W899 was in the development stage, Winter planned to price it at $130. In

preliminary discussions with customers about the W899 design, no resistance was detected to

suggestions that the price might be $130. The $130 price was considerably higher than the

estimated variable cost of $70 per unit to produce the W899, and it would provide Winter with

ample profits.

Shortly before setting the price of the W899, Winter discovered that a competitor was

reading a product very similar to the W899 and was no more than 60 days behind Winterâ€™s own

schedule. No information could be obtained on the competitorâ€™s planned price, although it had a

reputation for aggressive pricing. Worried about the competitor, and unsure of the market size,

Winter lowered the price of the W899 to $100. It maintained the price although, to Winterâ€™s

surprise, the competitor announced a price of $130 for its product.

After reviewing the 2010 sales of the W899, Winterâ€™s management concluded that unit

sales would have been the same if the product had been marketed at the original price of $130

each. Management has predicted that 2011 sales of the W899 would be either 85,000 units at

$100 each or 60,000 units at $130 each. Winter has decided to raise the price of the disk drive to

$130 effective immediately.

Having supported the higher price from the beginning, Sharon Daley, Winterâ€™s marketing

director, believes that the opportunity cost of selling the W899 for $100 during 2010 should be

reflected in the companyâ€™s internal records and reports. In support of her recommendation,

Daley explained that the company has booked these types of costs on other occasions when

purchase discounts not taken for early payment have been recorded.

Required:

a. Define opportunity cost and explain why opportunity costs are not usually recorded.

b. Winter Companyâ€™s management is considering Sharon Daleyâ€™s recommendation to book

the opportunity costs and have them reflected in its internal records and reports. If one

were to record a nonzero opportunity cost, calculate the dollar amount of the opportunity

cost that would be recorded by Winter Company for 2010 and explain how this cost

might be reflected on its internal reports.

c. Explain the impact of Winter Companyâ€™s selection of the $130 selling price for the W899

on 2011 operating income. Support your answer with appropriate calculations.

Source: CMA adapted

2-11: Make/Buy and the Opportunity Cost of Freed Capacity

Leland Manufacturing uses 10 units of part KJ37 each month in the production of radar

equipment. The cost to manufacture one unit of KJ37 is presented in the accompanying table.

Direct materials $ 1,000

Materials handling (20% of direct material cost 200

Direct labor 8,000

Manufacturing overhead 12,000

Total manufacturing cost $21,200

Materials handling represents the direct variable costs of the receiving department and is applied

to direct materials and purchased components on the basis of their cost. This is a separate charge

in addition to manufacturing overhead. Lelandâ€™s annual manufacturing overhead budget is onethird variable and two-third fixed. Scott Supply, one of Lelandâ€™s reliable vendors, has offered to

supply part KJ37 at a unit price of $15,000. The fixed cost of producing KJ37 is the cost of a

special piece of testing equipment that ensures the quality of each part manufactured. This

testing equipment is under a long-term, noncancelable lease. If Leland were to purchase part

KJ37, materials handling costs would not be incurred.

Required:

a. If Leland purchases the KJ37 units from Scott, the capacity Leland was using to

manufacture these parts would be idle. Should Leland purchase the parts from Scott?

Make explicit any key assumptions.

b. Assume Leland Manufacturing is able to rent all idle capacity for $25,000 per month.

Should Leland purchase from Scott Supply? Make explicit any key assumptions.

c. Assume that Leland Manufacturing does not wish to commit to a rental agreement but

could use idle capacity to manufacture another product that would contribute $52,000 per

month. Should Leland manufacture KJ37? Make explicit any key assumptions.

Source: CMA adapted

2-12: Analyzing the Results from a Cost Regression Model

An industrial engineer has been studying the cost behavior of the automated oil cooling

system in the numerically controlled cutting machine department. The oil cooling system

circulates oil across the cutting tools as the machines make parts. Besides cooling the tools, the

oil washes away cuttings. The oil system circulates the oil and separates out the cuttings, adds

new oil as needed, and recycles the old oil. The system serves 10 machines.

Oil consumption has varied widely over the last few months, and management worries

that the system is out of control. The industrial engineer has collected from the accounting

reports monthly cost data on the oil used in the system over the last five years. The oil cost data

represent monthly oil purchases. These cost data, combined with the number of machine cutting

hours in the month (total number of machine hours spent cutting parts in the month), led to the

following regression results (both series were entered as positive numbers):

Oil cost

in month t

ïƒ¦ï€

ïƒ¨ï€

ïƒ§ï€ ïƒ¶ï€

ïƒ¸ï€ ï€½ ï€1 2,675ï€1 6.5 4 x

Number of machine

cutting hours in month t

ïƒ¦ï€

ïƒ¨ï€

ïƒ§ï€ ïƒ¶ï€

ïƒ¸ï€

Based on the results of estimating this regression, the engineer concludes that the oil

cooling system is out of control and a major engineering study of the system is warranted.

Interpret the regression results. Based on your interpretation, is an engineering study of

the oil system warranted?

2-1: Solution to Fixed, Variable, and Average Costs (15 minutes)

a. The president of the university has calculated the average cost of each student. If the

decision is to add more students, the president should be looking at the marginal cost of

another student. The marginal cost can be approximated by the variable cost as long as

the university is below capacity.

b. The cost of adding 100 students is $300,000. Therefore, the variable cost per unit is

$300,000/100, or $3,000/student. The total variable cost of 4,000 students is (4,000

students)($3,000/student) or $12,000,000. The remaining cost at 4,000 students is

$30,000,000 – $12,000,000 or $18,000,000, which is equal to the fixed costs.

2-2: Solution to Opportunity Costs (10 minutes)

The monthly opportunity cost of operating a homeless shelter is:

Full-time employee $1,200

Supplies 400

Use of space (forgone revenue: (5 parties)($200/party) 1,000

Increase in utilities $1,300 – $1,000 300

Total $2,900

2-3: Solution to Fixed and Variable Costs (15 minutes)

a. The variable cost of one more spectator is the cost of clean-up:

(2 minutes/60 minutes/hour)($8/hour) = $0.2667

b. The opportunity cost with 10,000 spectators is:

Cost of relocating the fencing match $ 200

Cost of labor for preparation (20 hours)($8/hour) 160

Cost of additional utilities 500

Cost of clean-up (10,000)($0.2667) 2,667

Total $3,527

c. The opportunity cost with 12,000 spectators is:

Cost of relocating the fencing match $ 200

Cost of labor for preparation (20 hours)($8/hour) 160

Cost of additional utilities 500

Cost of clean-up (12,000)($0.2667) 3,200

Total $4,060

2-4: Solution to Opportunity Cost of Attracting Industry (15 minutes)

a. The headlines are not an accurate portrayal of the deal with Itagi. The analysis should

consider the alternative of not having Itagi come to town. Compared to the alternative,

Wellville is only paying $50,000 to buy the land and losing the property taxes on 20 acres

of undeveloped land, which is probably quite small.

b. The opportunity benefits to the town of Wellville include increased jobs and increased

property taxes after the first five years. The opportunity costs include increased

congestion and the cost of increased city services. The problems associated with

becoming a larger community should also be considered.

2-5: Solution to Cost, Volume, Profit Analysis (20 minutes)

a. Break-even point of Factory A = $20,000,000/($0.18 – $0.10) = 250,000,000 board-feet

b. To achieve an after-tax profit of $2,000,000:

[$10,000,000 + ($2,000,000/(1 – .3))]/($0.18 – $0.12) = 14,285,717 board-feet

c. Factory A has higher fixed costs, but lower variable costs per unit because of its larger

capacity. If the demand for lumber is lower than expected, Factory A will have a more

difficult time recovering its fixed costs. The break-even point for factory B is lower than

the break-even point for factory A. Therefore, Factory A is the riskier investment.

d. The after-tax profits of the two factories will be the same when:

(1 – .3)[($0.18 – $0.10)(Quantity) – $20,000,000]

= (1 – .3)[($0.18 – $0.12)(Quantity) – $10,000,000]

Quantity = 500 million board feet

2-6: Solution to Cost, Volume, Profit Analysis (20 minutes)

a. Through the postal system, the variable cost per unit is $10 + $2 or $12. Therefore, the

break-even point is:

$3,000/($20 – $12) = 375 handbags

b. The fixed costs through the freight company are $3,000 + $1,000 or $4,000 if fewer than

1,000 bags are purchased. The variable cost is only the $10 purchase cost. To make a

profit of $1,000, Leslie must buy and sell:

($4,000 + $1,000)/($20 – $10) = 500 handbags

c. The two methods would yield the same profit for the following quantity of handbags:

($20 – $12)(Quantity) – $3,000 = ($20 – $10)(Quantity) – $4,000

Quantity = 500 handbags

d. The 1,000 handbags will be most cheaply transported by container. Leslie’s trip expenses

of $3,000 will occur anyway, so they are not relevant for pricing the special order. The

incremental cost of the additional 1,000 handbags is the cost of the container ($1,000)

and the purchase cost of the handbags ($10/handbag)(1,000 handbags) or a total of

$11,000. If the special order has no other effect on long term sales, then Leslie should

accept a sales price above the $11,000 incremental cost.

2-7: Solution to Cost, Volume, Profit Analysis (CMA adapted) (45 minutes)

a.

Kalifo Company

Budgeted Net Income for 1996

Hedge Leaf

Weeders Clippers Blowers Total

Unit selling price $ 28.00 $ 36.00 $ 48.00

Variable manufacturing

cost $ 13.00 $ 12.00 $ 25.00

Variable selling cost 5.00 4.00 6.00

Total variable costs $ 18.00 $ 16.00 $ 31.00

Contribution margin $ 10.00 $ 20.00 $ 17.00

Unit sales 50,000 50,000 100,000

Total Contribution $500,000 $1,000,000 $1,700,000 $3,200,000

Fixed factory overhead 2,000,000

Fixed selling and

administrative expense 600,000

Total fixed costs 2,600,000

Income before taxes 600,000

Income taxes @ 40% 240,000

Budgeted net income $ 360,000

b.

Unit Sales Proportional

Contribution Proportion Contribution

Weeders $10.00 .25 $ 2.50

Hedge Clippers 20.00 .25 5.00

Leaf Blowers 17.00 .50 8.50

Proportional contribution margin/bundle $16.00

Total unit sales to breakeven =

Total fixed costs

Proportional contribution

=

$2,600,000

$16

= 162,500 units

Sales Total Product

Proportion Unit Sales Line Sales

Weeders .25 162,500 40,625

Hedge Clippers .25 162,500 40,625

Leaf Blowers .50 162,500 81,250

c.

Selling Sales Proportional

Price Proportion Selling Price

Weeders $28.00 .25 $ 7.00

Hedge Clippers 36.00 .25 9.00

Leaf Blowers 48.00 .50 24.00

Proportional selling price $40.00

Contribution margin rate =

Proportional contribution

Proportional selling price

=

$16

$40

= 40 percent

Total dollar sales =

Fixed costs + After-tax income (1 tax rate)

Contribution margin rate

ï‚¸ ï€

=

$450,000 $2,600,000

.6

.4

ï€«

=

$3,350,000

.4

= $8,375,000

d.

Unit Sales Proportional

Contribution Proportion Contribution

Weeders $10.00 .20 $ 2.00

Hedge Clippers1 19.00 .20 3.80

Leaf Blowers2 12.00 .60 7.20

Total proportional contribution

margin $13.00

Total unit sales to breakeven =

Total fixed costs

Total proportional contribution

=

$2,600,000

$13

= 200,000 units

Sales Total Product

Proportion Unit Sales Line Sales

Weeders .20 200,000 40,000

Hedge Clippers .20 200,000 40,000

Leaf Blowers .60 200,000 120,000

1 Variable selling costs increase; thus the unit contribution decreases to $19 [$36 â€“ ($12 + 4 + 1)].

2 The variable manufacturing cost increase 20 percent; thus, the unit contribution decreases to $12 [$48 â€“ (1.2 Ă—

25) â€“ 6].

e. Sylvia Harlow should consider the following limitations when using cost-volume-profit

analysis to evaluate Kalifo Company’s 1996 budget. This type of analysis assumes that:

â€¢ all costs are either fixed or variable or can be broken down into fixed and variable

components.

â€¢ all costs are linear in the relevant range, i.e., variable costs change in total with a

change in activity and fixed costs remain the same at all levels of output and sales in

the relevant range.

â€¢ sales prices will not change and sales demand is unlimited at the unit selling prices.

2-8: Solution to Breakeven and Cost Volume Profit with Taxes (CMA adapted) (15

minutes)

a. Breakeven =

$600,000

$16-12

= 150,000 units

b. Sales 200,000 Ă— 16 Ă— 1.1 $3,520,000

Variable Costs 200,000 Ă— 12 Ă— 1.1 (2,640,000)

Fixed Costs (600,000)

Net income before tax 280,000

Taxes (112,000)

Net income after taxes 168,000

Net income @ 200,000 units 120,000

Increase in net income $ 48,000

c. Let Q = unit sales. Then,

(16Q â€“ 1.3 Ă— 10Q â€“ 2Q â€“ 600,000) (60%) = 120,000

Q â€“ 600,000 = 200,000

Q = 800,000

PQ = $16 Ă— 800,000 = $12,800,000

2-9: Solution to Cost-Volume-Profit of a Make/Buy Decision (CMA adapted) (15 minutes)

a. Each month Elly incurs $150,000 of fixed cost to have capacity to produce 84,000 units.

They are only using 30,000 units of that capacity now. If they outsource MR24, they

will continue to incur 40% of the fixed costs, or $60,000. However, they save $90,000

($150,000 – $60,000). Besides saving the fixed costs they save $330,000 of variable

costs ($11 Ă— 30,000) or a total cost savings of $420,000. To be indifferent between

outsourcing and continuing to produce, the outside price must be $14 ($420,000 Ă·

30,000). An alternative way to solve the problem and get the same answer is:

40% of Fixed Cost Fixed Cost Outside Price + = Variable Cost +

30,000 Units 30,000 Units

$150,000 $150,000 40% P = $11 + = $14.00

30,000 30,000

ï‚´

ï€

b. $12.875 +

40% of Fixed Cost $150,000 = $11 +

Q Units Q Units

$12.875Q + $60,000 = $11Q + $150,000

$1.875Q = $90,000

Q = 48,000 units

2-10: Solution to Opportunity Cost of Purchase Discounts and Lost Sales(CMA adapted)

(20 minutes)

a. Opportunity cost is defined as the profit that could have been realized if a particular

action was not chosen. Opportunity costs occur because a firm is faced with alternative

uses of resources.

Opportunity costs are not ordinarily incorporated in formal accounting systems

because

â€¢ they do not involve cash receipts or outlays (absence of a transaction).

â€¢ the next best opportunity is often difficult to determine.

â€¢ these types of costs often are not readily measurable.

b. Opportunity cost in 2008 = Units sold Ă— Opportunity cost per unit

Units sold = Revenue

Unit sales price

=

$5,000,000

$100

= 50,000 units sold

= 50,000 Ă— ($130â€“100)

= $1,500,000 opportunity cost in 2006

If the opportunity cost of Winter’s pricing decision were to be reported in the revenue

section of Winter’s income statement, it would appear as shown below (there would be no

change in Winter’s net income for 2010):

Revenue (50,000 Ă— $130) $6,500,000

Loss from product pricing

(50,000 Ă— $30) 1,500,000

Net revenue $5,000,000

c. The selection of the $130 selling price for the W899 will increase Winter’s 2011

operating income by $1,050,000. This is equal to the increase in total contribution shown

in the analysis of the 2011 projected sales of the W899 presented below.

$100 Selling Price $130 Selling price

Revenue per unit $100 $130

Variable cost per unit 70 70

Contribution margin per unit $ 30 $ 60

Total contribution:

At $130 selling price

60,000 units Ă— $60 = $3,600,000

At $100 selling price

85,000 units Ă— $30 = 2,550,000

Net gain in total

contribution = $1,050,000

2-11: Solution to Make/Buy and the Opportunity Cost of Freed Capacity (CMA adapted)

(20 minutes)

a. Cost of outside purchase:

Payment to Scott $15,000

Continuing cost of idle capacity

(12,000 Ă— 2/3) 8,000

$23,000

Cost if continue to make: 21,200

Incremental cost of purchase $ 1,800

Explicit assumption: the two-thirds of the fixed manufacturing overhead ($8,000) is not a

sunk cost and will still be incurred if the facility is idle.

b. Cost of outside purchase:

Payment to Scott $15,000

Continuing cost of capacity 8,000

Lease receipts ($25,000 Ă· 10 units) (2,500)

Net cash outlay of purchase 20,500

Cost if continue to make 21,200

Incremental cost of making $ 700

Explicit assumption: the two-thirds of the fixed manufacturing overhead ($8,000) is not a

sunk cost and will still be incurred if the facility is idle.

c. Cost of outside purchase:

Payment to Scott $15,000

Continuing cost of capacity 8,000

Contribution from new product ($52,000 Ă· 10 units) (5,200)

Net cash outlay from purchase $17,800

Cost in continue to make 21,200

Incremental cost of manufacturing $ 3,400

2â€“12: Solution to Analyzing the Results from a Cost Regression Model (20 minutes)

The regression results, on their surface, indicate that both fixed costs and variable costs

per unit are negative. These findings are counter-intuitive. However, based on the regression

one cannot conclude that the system is out of control. Several econometric problems can cause

estimated fixed costs and variable costs to have negative point estimates, including the

following:

1. The data have not been adjusted for price-level changes, causing the residuals to be

serially correlated. While serially-correlated residuals do not cause the estimated

coefficients to be biased, they will be measured with extremely large error.

2. The quantity of oil consumed depends on cutting time. But, the cost of oil is the product

of price and quantity. Ideally, the dependent variable should be the quantity of oil

consumed, not cost. At least this should control for price fluctuations, which again

increase the sampling variability of the estimated coefficients.

3. Monthly oil cost data likely vary over the year if the business is seasonal. This again

induces autocorrelation into the residuals, unless some adjustments are made.

4. Using the last five years of data assumes that the same system has been in operation for

the last five years with no changes in technology or types of machines using the oil

system. That is, the underlying process must have been stationary in order to use five

years of data. This is unlikely to have been true.

5. Another critical assumption underlying the regression is that all of the cutting machines

using the oil system are homogeneous and thus an hour of cutting time on each consumes

roughly the same amount of oil.

6. The accounting system records oil purchases and not necessarily oil consumption in any

given month. If oil is not inventoried when purchased but rather is expensed, then there

is a mismatch between oil consumption and oil cost. This mismatch introduces further

errors into the regression and increases the imprecision of the estimated fixed and

variable costs.

One should look at the reported standard errors of the estimated coefficients. Given the

preceding problems, the standard errors are probably large relative to the estimated coefficients

suggesting that one cannot conclude that the coefficients are non-zero. While a detailed

engineering study might be warranted, aberrations in the data are likely causing the estimated

coefficients to be measured with substantial error thus making any inferences drawn from the

results meaningless.